Answer:
x = 24.10
Step-by-step explanation:
The given sides of the triangle are the hypotenuse (x) and a side of length 20 that is adjacent to the 34° angle and opposite the 56° angle.
The mnemonic SOH CAH TOA reminds you of relationships between the <em>hypotenuse</em> and <em>adjacent</em> or <em>opposite</em> sides:
Sin = Opposite/Hypotenuse
Cos = Adjacent/Hypotenuse
If we want to use the "adjacent" side, we would choose ...
cos(34°) = 20/x
x = 20/cos(34°) ≈ 20/0.83 ≈ 24.10 . . . . . rounding according to instructions
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If we want to use the "opposite" side, we would choose ...
sin(56°) = 20/x
x = 20/sin(56°) ≈ 20/0.83 ≈ 24.10 . . . . . rounding according to instructions
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<em>Comment on rounding</em>
If you round correctly (only at the last step), the proper answer is 24.12.
